Properties of Light

Separation of light and dark by Michelangelo (Sistine chapel, the Vatican)                  

There are many different types of light, red, yellow, green, blue, violet... In addition, there are many types of light not visible to naked eyes: radio waves, microwaves, infra-red light, ultra-violet light, x-rays, gamma-rays. To see what kind of light we have at hand, we can break visible light into its components by using a prism (or a diffraction grating). This produces a spectrum.

One may thing all these are quite different. In fact, remarkable, they all have precisely the same nature. They are nothing but electromagnetic waves, the only difference being their wavelength.

Having a wave character means that light is characterized by a wavelength L or a frequency f. All forms of light travel precisely at the same velocity: the speed of light

c = 300.000 km/sec,

which also defines the relation between wavelength and frequency

c=L*f.

Three Types of Spectra: the Fingerprints of Light

If we look at the colors of light coming from different sources, we can see several different spectra, as follows:

a) "Black-body" (continious) spectra - all colors found.

b) Discrete (line) "absorption" spectra - only several colors missing.

c) Discrete (line) "emission" spectra - only several colors found.

What is the origin of these different spectra??? Let us take a closer look at these spectra and their origin.

Radiation from a heated object: "Black body radiation"

Observing the light spectrum emitted by a distant object- such as our Sun- is an  important diagnostic tool. For example, we can determine the temperature of the  Sun in an accurate way by observing its distribution of colors. The main assumption  behind this hypothesis is that the temperature of an object (essentially how hot it  is) is related, at the atomic level, with the motion of the atoms it contains. The hotter  the object the more rapidly the atoms vibrate (or rattle). These rapid vibrations  cause atomic collisions which are responsible for exciting electrons from their  ground state into some excited states. Eventually, the electrons get de-excited  an emit photons, or electromagnetic radiation. This kind of radiation is called  black-body radiation because it refers to light emitted by an ideal object that is  a perfect absorber or emitter of radiation. Many astronomical bodies, including
stars, emit black-body radiation, as if they were perfect absorbers/emitters.

If you study the light emitted from our Sun - a typical star - you will observe  an electromagnetic spectrum similar to one of the three shown in the above  figure. Depending on the temperature of the star the maximum, or peak, of  the distribution of light will be at a specific wavelength and color. For example, a star  with a (surface) temperature of 5000 degrees Kelvin will have the peak of  its radiation emitted at 600 nm - or in the yellow part of the visible spectrum.  Remember that you can convert to degrees Kelvin - an absolute temperature  scale - by simply adding the number 273 to the temperature in degrees Celsius.  Computing the temperature of the object emitting the radiation is not difficult.  You simply take the wavelength (expressed in nanometers) where you see  the peak in the radiation spectrum (L_max ) and compute the temperature T  (in degrees Kelvin) by using

Wien's law:  T=3,000,000/L_max  

Similarly, if one knows the temperature of an object - such as you - one  can compute the wavelength at which ones emitted spectrum will peak. For  example,  our external temperature is close to the ambient temperature of, say,  27 degrees Celsius. To convert to degrees Kelvin you simply add the number  273. Hence, a temperature of 27 degrees Celsius corresponds to 300 Kelvin.  Then L_max=3,000,000/300=10,000 nanometers = 10^-5 m. This wavelength  is in the infrared part of the spectrum. Hence, your "body glow" is invisible  to you and me - but probably not to rattlesnakes!
 

Finally, one last important formula. You can compute the total energy radiated  by a black-body every second and per square meter of area by using the

Stefan-Boltzmann Law:  E = s T⁴

As you may suspect, s is yet another  constant  - the  so-called Stefan-Boltzmann constant  - which is given by  s=5.67 x 10^-8 Joules/m²/sec degree⁴ . Hence, an object with a temperature  twice as large as our Sun will emit 16 times as much radiation.

Atoms and Starlight

To understand absorption and emission spectra, we need to learn a few facts about atoms producing them.

Matter is made out of atoms and there are over a hundred different atoms. Various atoms can bind together to form molecules and molecules bind to make complex compound. Because of their tiny size (only 10^-10 meters) a quantity of a given substance can be observed with the naked eye only when it contains of the order of  10²³ = 100,000,000,000,000,000,000,000 such atoms or molecules.

An atom has a nucleus and electrons - which are moving in shells around the nucleus. Thus, an atom resembles a "miniature" planetary system with the nucleus playing the role of the Sun and the electrons that of the planets. The nucleus is made of protons and neutrons, which themselves are made of even smaller particles called quarks. The protons have positive electric charge while the electrons carry negative charge. Neutrons are electrically neutral (they carry no electric charge).  An electrically neutral atom is more stable when it has equal number of electrons and protons.  The attractive Electric force between the positively-charged protons in the nucleus and the negatively-charged electrons binds the electrons and make them move in shells around the nucleus.

Atoms - and therefore you and me - are mostly empty space! If you would take the atomic nucleus and make it as large as a Basketball,  then the innermost electron will be located on the bleachers at Doak Campbell Stadium. The simplest atom in nature is the Hydrogen atom,  having one proton, no neutron, and just one electron revolving around the nucleus. The next simplest element is Helium and the most  abundant form of helium is the isotope helium-4 having two protons  and two neutrons in the nucleus, and two electrons.

Atomic excitations

One of the main departures from the solar system analogy of the atom is that, while planets can revolve around the Sun in any specific orbit, the shells in which the electrons move in an atom are fixed and characterized by an energy level; the lowest energy level is called the ground state. The fundamental reason underlying this effect must be explained with Quantum
Mechanics - a theory that even Newton was not aware of - and one of the highest theoretical achievements of the 20th Century Physics. The permitted orbits (or shells) that electrons can occupy are like steps in a staircase or apartment in a building; you can live in apartment one or apartment two - but definitely you can not live in apartment number one-and-one-half. However,  if an electron  in an atom receives energy from outside the atom,  the electron can make a transition to an outer shell, in the same way that you can take the elevator on the first floor (your orbit or shell) and go to the third floor. Being in an outer orbit (or being in a higher floor) is refereed to being in an excited state. The electron stays in such an excited state only for a very short time and eventually returns to its ground state by emitting a photon (the quanta of light) which carries the energy lost in the transition. A photon is a particle of light and at the same time an electromagnetic wave.

Origin of absorption spectra

Generally the absorption spectrum looks as follows. Photons of only the proper  wavelengths can be absorbed by the gas atoms and then are re-emitted in random  directions. Most of these re-emitted photons will not reach the telescope and the  spectrum will be missing some "colors".

Origin of emission spectra

Generally an emission spectrum is obtained as follows. Pointing the telescope away from the bulb, we can receive only those photons the atoms can absorb and then re-emit, producing emission lines in the spectrum.

The Lagoon Nebula in Sagittarius is a cloud of gas and dust about 60 light-years in diameter. Its gases (mostly Hydrogen) are excited by  the ultraviolet radiation of the hot, young stars within, and it glows in the pink - produced by the mixture of red (656 nm) the blue (486 nm)  and the violet (434 and 410 nm) Balmer lines.